A348067 - OEIS

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A348067

Matula-Goebel tree number of tree n with a new leaf added below each existing vertex.

2, 6, 26, 18, 202, 78, 122, 54, 338, 606, 2462, 234, 794, 366, 2626, 162, 1346, 1014, 502, 1818, 1586, 7386, 4546, 702, 20402, 2382, 4394, 1098, 8914, 7878, 43954, 486, 32006, 4038, 12322, 3042, 2962, 1506, 10322, 5454, 12178, 4758, 4946, 22158, 34138, 13638 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	COMMENTS	`k times nested a(a(...a(1))) = A076146(k+1) is the Matula-Goebel number of the binomial tree order k constructed by an "expansion" method starting from a singleton and successively adding a new leaf under every vertex.`
	LINKS	`Kevin Ryde, Table of n, a(n) for n = 1..5000` `Index entries for sequences related to Matula-Goebel numbers`
	FORMULA	`a(n) = 2 * Product_{i=1..k} prime(a(primepi(p[i]))), where n = p[1]...p[k] is the prime factorization of n with multiplicity (A027746).`
	EXAMPLE	`tree n=6 tree a(6) = 78` `R R___ root R` `\| \ \|\ \` `A B A @ B new vertices` `\| \|\ \ "@" below each` `C C @ @ existing` `\` `@`
	PROG	`(PARI) a(n) = my(f=factor(n)); 2*factorback([prime(self()(primepi(p))) \| p<-f[, 1]], f[, 2]);`
	CROSSREFS	`Cf. A027746 (prime factors), A076146 (binomial tree).` `Cf. A297002 (add leaves under children of the root).` `Sequence in context: A178087 A109286 A009466 * A032479 A029988 A050573` `Adjacent sequences: A348064 A348065 A348066 * A348068 A348069 A348070`
	KEYWORD	`nonn`
	AUTHOR	`Kevin Ryde, Oct 01 2021`
	STATUS	`approved`

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Last modified June 26 00:12 EDT 2022. Contains 354870 sequences. (Running on oeis4.)